Your post was sadly lacking in DOB, DOM, etc. You should find some of these AUS civil/church rcds.
I research the Irish Family History Foundation's database. It contains 12,000,000 surviving rcds for abt 65% of Irish counties. Rcds are increasingly sparse B4 1840, rare B4 1800.
Note 1 - Without a KNOWN parish, the chance of an ancestor's rcds NOT being in this database is AT LEAST 35%.
Note 2 - Only 1/2 of Co. Cork's rcds are in this database.
Note 3 - The RC church kept control over most parish rcds from Tipperary (north). These are ONLY available thru the Tipperary Family History Research center at a substantial fee (regardless of outcome).
For John Toohey B ???? in Co. Tipperary with a father forenamed William, I found 2 possible rcds: 1839 and 1843.
For William Toohey M ???? in Co. Tipperary, I found 6 possible M rcds: 1824, 1826, 1834, 1838, 1845, 1847 and 1849.
For Mary Noon M ???? in Co. Tipperary, I found 1 M rcd in 1844. This doesn't correlate with the M rcds for William.
Note - 3 may apply here. This has been a particularly nasty fly in my genealogical ointment.
Google the Foundation's name to lead you to this database. Register, opt to be notified as rcds are added and browse. Pls post your search results to my genforum msg.